155
155

Oct 16, 2017
10/17

by
3Blue1Brown

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Complementary video on MinutePhysics: https://youtu.be/zcqZHYo7ONs Learn more through active problem-solving at Brilliant: https://brilliant.org/3b1b Special thanks to these patrons: http://3b1b.co/light-quantum-thanks Huge thanks to my friend Evan Miyazono, both for encouraging me to do this project, and for helping me understand many things along the way. This is a simple primer for how the math of quantum mechanics, specifically in the context of polarized light, relates to the math of...

Topics: Youtube, video, Education, Mathematics, three blue one brown, 3 blue 1 brown, 3b1b, quantum...

7
7.0

Apr 29, 2019
04/19

by
3Blue1Brown

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An animated introduction to the Fourier Transform. Home page: https://www.3blue1brown.com/ Brought to you by you: http://3b1b.co/fourier-thanks Puzzler at the end by Jane Street: https://janestreet.com/3b1b Follow-on video about the uncertainty principle: https://youtu.be/MBnnXbOM5S4 Interactive made by a viewer inspired by this video: https://prajwalsouza.github.io/Experiments/Fourier-Transform-Visualization.html ------------------ Animations largely made using manim, a scrappy open source...

Topics: Youtube, video, Education, Mathematics, fourier transform, three blue one brown, three, 3 blue 1...

18
18

Dec 26, 2012
12/12

by
[dirección, Sergio Sánchez Cerezo].

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Topics: Statistics, Business mathematics, Commercial statistics, Business mathematics, Commercial...

1,003
1.0K

Feb 16, 2009
02/09

by
[Newton, Isaac, Sir], 1642-1727; Jones, W. (William), 1675-1749

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Book digitized by Google from the library of Ghent University and uploaded to the Internet Archive by user tpb.

Topics: Mathematics, Calculus, Curves, Cubic

Source: http://books.google.com/books?id=VTgPAAAAQAAJ&oe=UTF-8

1,828
1.8K

Mar 4, 2009
03/09

by
[Pozzo, Agostino dal] [from old catalog]; Pre-1801 Imprint Collection (Library of Congress) DLC [from old catalog]

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Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

Topics: Mathematics, Astronomy, Astronomy

Source: http://books.google.com/books?id=ofdJAAAAMAAJ&oe=UTF-8

2
2.0

Jun 30, 2018
06/18

by
A Abbas; A Assi; Pedro A Garcıa-Sánchez

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Let K be a field and denote by K[t], the polynomial ring with coefficients in K. Set A = K[f1,. .. , fs], with f1,. .. , fs $\in$ K[t]. We give a procedure to calculate the monoid of degrees of the K algebra M = F1A + $\times$ $\times$ $\times$ + FrA with F1,. .. , Fr $\in$ K[t]. We show some applications to the problem of the classification of plane polynomial curves (that is, plane algebraic curves parametrized by polynomials) with respect to some oh their invariants, using the module of...

Topics: Algebraic Geometry, Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1703.02825

2
2.0

Jun 29, 2018
06/18

by
A Al-Ghassani; R Halburd

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Consider the discrete equation $$ y_{n+1}+y_{n-1}=\frac{a_n+b_ny_n+c_ny_n^2}{1-y_n^2}, $$ where the right side is of degree two in $y_n$ and where the coefficients $a_n$, $b_n$ and $c_n$ are rational functions of $n$ with rational coefficients. Suppose that there is a solution such that for all sufficiently large $n$, $y_n\in\mathbb{Q}$ and the height of $y_n$ dominates the height of the coefficient functions $a_n$, $b_n$ and $c_n$. We show that if the logarithmic height of $y_n$ grows no...

Topics: Exactly Solvable and Integrable Systems, Number Theory, Dynamical Systems, Nonlinear Sciences,...

Source: http://arxiv.org/abs/1601.03100

0
0.0

Jun 29, 2018
06/18

by
A Brault; L Dumas; D Lucor

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SUMMARY This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation model. A simple pulsatile output form is utilized to reproduce the most relevant cardiac features with a minimum number of parameters associated with left ventricle dynamics. Another source of critical uncertainty is the spatial heterogeneity of the aortic...

Topics: Medical Physics, Numerical Analysis, Analysis of PDEs, Physics, Mathematics

Source: http://arxiv.org/abs/1606.06556

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6.0

Jun 28, 2018
06/18

by
A Djaballah; Alexandre Chapoutot; Michel Kieffer; O Bouissou

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Recently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe subset in which the state can be proved to remain and the complementary subset containing some unsafe region. This approach does not require any reachability analysis, but needs the computation of a valid barrier function, which is difficult when considering...

Topics: Systems and Control, Computing Research Repository, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1506.05885

0
0.0

Jun 28, 2018
06/18

by
A Doliwa; A M Grundland

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The main objective of this paper is to derive the Enneper-Weierstrass representation of minimal surfaces in $\mathbb{E}^3$ using the soliton surface approach. We exploit the Bryant-type representation of conformally parametrized surfaces in the hyperbolic space $H^3(\lambda)$ of curvature $-\lambda^2$, which can be interpreted as a 2 by 2 linear problem involving the spectral parameter $\lambda$. In the particular case of constant mean curvature-$\lambda$ surfaces a special limiting procedure...

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1511.02173

3,320
3.3K

Nov 13, 2012
11/12

by
A First Course in Design and Analysis of Experiments

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A First Course in Design and Analysis of Experiments

Topics: general mathematics, experiment, design, comparisons, factorial data, math

0
0.0

Jun 29, 2018
06/18

by
A Ghose-Choudhury; Partha Guha

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This paper is concerned with the monotonicity of the period function for closed orbits of systems of the Li\'enard II type equation given by $\ddot{x} + f(x)\dot{x}^{2} + g(x) = 0$. We generalize Chicone's result regarding the monotonicity of the period function to planar Hamiltonian vector fields in the presence of a position dependent mass. Sufficient conditions are also given for the isochronicity of the potential in case of such a system.

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1608.02910

0
0.0

Jun 30, 2018
06/18

by
A Hartmann; X Massaneda; A Nicolau

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We show that a discrete sequence $\Lambda$ of the unit disk is the union of $n$ interpolating sequences for the Nevanlinna class $N$ if and only if the trace of $N$ on $\Lambda$ coincides with the space of functions on $\Lambda$ for which the divided differences of order $n - 1$ are uniformly controlled by a positive harmonic function.

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1702.04974

15
15

Feb 27, 2019
02/19

by
A K Bag

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The observations of Al-Biruni on some of the topics and concepts of Indian Arithmetic namely numerals, decimal place-value, the use of dust numerals, Indian Arithmetic in Arabia, rule of three, Fraction has been analysed in this book.

Topics: Indian Mathematics, Arabic Numerals

0
0.0

Jun 30, 2018
06/18

by
A K Rathie; R B Paris

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Expressions for the summation of the series involving the Laguerre polynomials \[S_m(\pm\nu, \pm p)\equiv e^{-x}\sum_{n=0}^\infty \frac{x^n\,L_n^{(\nu)}(x)}{(1\pm \nu\pm p)_n}\frac{(f+m)_n}{(f)_n}\] for any non-negative integers $m$ and $p$ are obtained in terms of generalized hypergeometric functions. These results extend previous work in the literature.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1411.5257

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0.0

Jun 29, 2018
06/18

by
A Kachmar; P Keraval; N Raymond

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This paper is devoted to establish semiclassical Weyl formulae for the Robin Laplacian on smooth domains in any dimension. Theirs proofs are reminiscent of the Born-Oppenheimer method.

Topics: Spectral Theory, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1602.06179

0
0.0

Jun 28, 2018
06/18

by
A M Semikhatov; I Yu Tipunin

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For the quantum walled Brauer algebra, we construct its Specht modules and (for generic parameters of the algebra) seminormal modules. The latter construction yields the spectrum of a commuting family of Jucys--Murphy elements. We also propose a Baxterization prescription; it involves representing the quantum walled Brauer algebra in terms of morphisms in a braided monoidal category and introducing parameters into these morphisms, which allows constructing a "universal transfer...

Topics: Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1512.06994

0
0.0

Jun 30, 2018
06/18

by
A Mani

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Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to obtain nice properties comparable to those of classical rough approximations. In this research paper, these ideas are generalized in a severe way by the present author and associated semantic features are investigated by her. Granules are used in the...

Topics: Logic, Computing Research Repository, Information Theory, Logic in Computer Science, Artificial...

Source: http://arxiv.org/abs/1704.05477

0
0.0

Jun 30, 2018
06/18

by
A Marzuoli; F A Raffa; M Rasetti

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We explore a variety of reasons for considering su(1,1) instead of the customary h(1) as the natural unifying frame for characterizing boson systems. Resorting to the Lie-Hopf structure of these algebras, that shows how the Bose-Einstein statistics for identical bosons is correctly given in the su(1,1) framework, we prove that quantization of Maxwell's equations leads to su(1,1), relativistic covariance being naturally recognized as an internal symmetry of this dynamical algebra. Moreover...

Topics: Quantum Physics, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1406.2908

0
0.0

Jun 30, 2018
06/18

by
A Mouze

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Let $(\lambda\_n)$ be a strictly increasing sequence of positive integers. Inspired by the notions of topological multiple recurrence and disjointness in dynamical systems, Costakis and Tsirivas have recently established that there exist power series $\sum\_{k\geq 0}a\_kz^k$ with radius of convergence 1 such that the pairs of partial sums $\{(\sum\_{k=0}^na\_kz^k,\sum\_{k=0}^{\lambda\_n}a\_kz^k): n=1,2,\dots\}$ approximate all pairs of polynomials uniformly on compact subsets...

Topics: Classical Analysis and ODEs, Complex Variables, Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1703.05004

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2.8K

Oct 16, 2018
10/18

by
A Pogorelov

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ABOUT THE BOOK This is a manual for the students of universities and teachers' training colleges. Containing the compulsory course of geometry, its particular impact is on elementary topics. The book is, therefore, aimed at professional training of the school or university teacher-to-be. The first part, analytic geometry, is easy to assimilate, and actually reduced to acquiring skills in applying algebraic methods to elementary geometry. The second part, differential geometry, contains the...

Topics: mathematics, geometry, analytic geometry, vectors, straight line, mir publishers, mir books, conic...

0
0.0

Jun 29, 2018
06/18

by
A Popier

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We study the behaviour at the terminal time T of the minimal solution of a backward stochastic differential equation when the terminal data can take the value +$\infty$ with positive probability. In a previous paper, we have proved existence of this minimal solution (in a weak sense) in a quite general setting. But two questions arise in this context and were still open: is the solution c{\`a}d{\`i}{\`a}g on [0,T] ? In other words does the solution have a left limit at time T ? The second...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1601.03186

0
0.0

Jun 30, 2018
06/18

by
A Sapora; M Codegone; G Barbero; LR Evangelista

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The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of hyperbolic type, in order to take into account the finite velocity of propagation of the density variations. We show that in this framework the condition on the conservation of the number of particles gives rise to a nonlocal boundary condition. We solve the partial...

Topics: Mathematics, Mathematical Physics, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1402.2853

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1.0

Jun 30, 2018
06/18

by
A Sinan Ozkan

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In this paper, we consider a Sturm--Liouville dynamic equation with Robin boundary conditions on time scale and investigate the conditions which guarantee that the potential function is specified.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1702.07298

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1.0

Jun 29, 2018
06/18

by
A V Jayanthan; N Narayanan; S Selvaraja

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Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. For all $s \geq 1$, we obtain upper bounds for reg$(I(G)^s)$ for bipartite graphs. We then compare the properties of $G$ and $G'$, where $G'$ is the graph associated with the polarization of the ideal $(I(G)^{s+1} : e_1\cdots e_s)$, where $e_1,\ldots e_s$ are edges of $G$. Using these results, we explicitly compute reg$(I(G)^s)$ for several subclasses of bipartite graphs.

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1609.01402

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0.0

Jun 29, 2018
06/18

by
A V Osipov; G Söderbacka

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In this paper we consider a family of system with 2 predators feeding on one prey. We show how to construct a positively invariant set in which it is possible to define a Poincar\'e map for examining the behaviour of the system, mainly in the case when both predators survive. We relate it to examples from earlier works.

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1604.07962

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2.0

Jun 30, 2018
06/18

by
A V Tsiganov

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We present auto and hetero B\"acklund transformations of the nonholonomic Veselova system using standard divisor arithmetic on the hyperelliptic curve of genus two. As a by-product one gets two natural integrable systems on the cotangent bundle to the unit two-dimensional sphere whose additional integrals of motion are polynomials in the momenta of fourth order.

Topics: Mathematics, Mathematical Physics, Nonlinear Sciences, Exactly Solvable and Integrable Systems,...

Source: http://arxiv.org/abs/1703.04251

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0.0

Jun 29, 2018
06/18

by
A-C Brunet; J-M Azais; J-M Loubes; J Amar; R Burcelin

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We propose a novel method to cluster gene networks. Based on a dissimilarity built using correlation structures, we consider networks that connect all the genes based on the strength of their dissimilarity. The large number of genes require the use of the threshold to find sparse structures in the graph. in this work, using the notion of graph coreness, we identify clusters of genes which are central in the network. Then we estimate a network that has these genes as main hubs. We use this new...

Topics: Quantitative Biology, Statistics, Quantitative Methods, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1607.01516

1
1.0

Jun 29, 2018
06/18

by
A-Ming Liu; Tongsuo Wu

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For each Boolean graph $B_n$, it is proved that both $B_n$ and its complement graph $\overline{B_n}$ are vertex decomposable. It is also proved that $B_n$ is an unmixed graph, thus it is also Cohen-Macaulay.

Topics: Commutative Algebra, Combinatorics, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1611.07574

1
1.0

Jun 29, 2018
06/18

by
A-Ming Liu; Tongsuo Wu

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Let $I$ be a graded ideal of $K[x_1,\ldots,x_n]$ generated by homogeneous polynomials of a same degree $d$, and assume that $I$ has linear quotients. In this note, we use Horseshoe Lemma to give a relatively direct inductive construction of a minimal free resolution of $I$, which is called a $d$-linear resolution.

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1610.00055

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37

Jul 29, 2018
07/18

by
A. (Alphonse) Rebière

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Book from Project Gutenberg: Mathématiques et Mathématiciens: Pensées et Curiosités

Topics: FR Sciences et Techniques, Quotations, French, Mathematicians -- France, Mathematics -- France --...

Source: https://www.gutenberg.org/ebooks/41991

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0.0

Jun 30, 2018
06/18

by
A. -H. Nokhodkar

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We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can be used to classify totally decomposable algebras with orthogonal involution. Also, using this form, a criterion is obtained for an orthogonal involution on a split algebra to be conjugated to the transpose involution.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1701.02169

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0.0

Jun 29, 2018
06/18

by
A. -K. Gallagher; T. Harz; G. Herbort

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A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of D'Angelo.

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1603.09099

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0.0

Jun 30, 2018
06/18

by
A. -K. Herbig; J. D. McNeal

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A sufficient condition for $\bar{\partial}$ to have closed range is given for pseudoconvex, possibly unbounded domains in $\mathbb{C}^n$.

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1410.3559

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2.0

Jun 27, 2018
06/18

by
A. -L. Basdevant; N. Enriquez; L. Gerin; J. -B. Gouéré

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We introduce two stationary versions of two discrete variants of Hammersley's process in a finite box, this allows us to recover in a unified and simple way the laws of large numbers proved by T. Sepp{\"a}l{\"a}inen for two generalized Ulam's problems. As a by-product we obtain an elementary solution for the original Ulam problem. We also prove that for the first process defined on Z, Bernoulli product measures are the only extremal and translation-invariant stationary measures.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1503.00507

1
1.0

Jun 30, 2018
06/18

by
A. A. Alikhanov

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We consider difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$, $\beta$ and $\gamma$. By the method of energy inequalities, for the solution of the difference problem, we obtain a priori estimates, which imply the stability and convergence of these difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems.

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1405.0030

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0.0

Jun 30, 2018
06/18

by
A. A. Alikhanov

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In this paper we construct a new difference analog of the Caputo fractional derivative (called the $L2$-$1_\sigma$ formula). The basic properties of this difference operator are investigated and on its basis some difference schemes generating approximations of the second and forth order in space and the second order in time for the time fractional diffusion equation with variable coefficients are considered. Stability of the suggested schemes and also their convergence in the grid $L_2$ - norm...

Topics: Mathematics, Numerical Analysis, Mathematical Physics

Source: http://arxiv.org/abs/1404.5221

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0.0

Jun 30, 2018
06/18

by
A. A. Ambily; Ravi A. Rao

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We prove that a quadratic $A[T]$-module $Q$ with Witt index ($Q/TQ$)$ \geq d$, where $d$ is the dimension of the equicharacteristic regular local ring $A$, is extended from $A$. This improves a theorem of the second named author who showed it when $A$ is the local ring at a smooth point of an affine variety over an infinite field. To establish our result, we need to establish a Local-Global Principle (of Quillen) for the Dickson--Siegel--Eichler--Roy (DSER) elementary orthogonal transformations.

Topics: Mathematics, K-Theory and Homology, Commutative Algebra

Source: http://arxiv.org/abs/1401.0809

0
0.0

Jun 30, 2018
06/18

by
A. A. Ambily

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In this paper, we prove the normality of the Roy's elementary orthogonal group (Dickson--Siegel--Eichler--Roy or DSER group) over a commutative ring which was introduced by A. Roy in [MR0231844] under some conditions on the hyperbolic rank. We also establish a stability theorem for $K_1$ of Roy's group. We obtain a decomposition theorem for the elementary orthogonal group which is used to deduce the stability theorem.

Topics: Mathematics, K-Theory and Homology, Commutative Algebra

Source: http://arxiv.org/abs/1401.0822

0
0.0

Jun 30, 2018
06/18

by
A. A. Ambily; Ravi A. Rao

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Let $(Q, q)$ be a quadratic space over a commutative ring $R$ in which $2$ is invertible, and consider the Dickson--Siegel--Eichler--Roy's subgroup $EO_{R}(Q, H(R)^{m})$ of the orthogonal group $O_R(Q \perp H(R)^m)$, with rank $Q= n \geq 1$ and $m\geq 2$. We show that $EO_{R}(Q, H(R)^{m})$ is a normal subgroup of $O_R(Q \perp H(R)^m)$, for all $m\geq 2$. We also prove that the DSER group $EO_{R}(Q, H(P))$ is a normal subgroup of $O_{R}(Q \perp H(P))$, where $Q$ and $H(P)$ are quadratic spaces...

Topics: K-Theory and Homology, Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1703.04083

0
0.0

Jun 30, 2018
06/18

by
A. A. Ardentov; Yu. L. Sachkov

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The left-invariant sub-Riemannian problem on the Engel group is considered. The problem gives the nilpotent approximation to generic nonholonomic systems in four-dimensional space with two-dimensional control, for instance to a system which describes motion of mobile robot with a trailer. The global optimality of extremal trajectories is studied via geometric control theory. The global diffeomorphic structure of the exponential mapping is described. As a consequence, the cut time is proved to...

Topics: Mathematics, Differential Geometry, Optimization and Control

Source: http://arxiv.org/abs/1408.6651

1
1.0

Jun 26, 2018
06/18

by
A. A. Beilinson

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We construct generalized quantum Cauchy pre-measures that correspond to the analytic continuation of the transition probability of the Cauchy process to imaginary time. We show that these complex pre-measures of time translations extend to a measure on the space dual to a real Hilbert space whose support is locally compact in the uniform convergence topology and with velocities in the Hilbert space. At that the quantum Cauchy-Dirac and Cauchy-Maxwell pre-measures of time translations of...

Topics: Quantum Physics, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1501.03750

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0.0

Jun 27, 2018
06/18

by
A. A. Beilinson

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The article describes a relation between the fundamental solutions of Dirac's equations for free electron and electron in given electromagnetic field viewed as functionals on bump functions. We explain how classical relativistic mechanics of a charged particle in given electromagnetic field arises from quantum mechanics of Dirac's electron in that field.

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1506.04034

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0.0

Jun 30, 2018
06/18

by
A. A. Belavin; V. A. Belavin

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We use the connection between the Frobrenius manifold and the Douglas string equation to further investigate Minimal Liouville gravity. We search a solution of the Douglas string equation and simultaneously a proper transformation from the KdV to the Liouville frame which ensure the fulfilment of the conformal and fusion selection rules. We find that the desired solution of the string equation has explicit and simple form in the flat coordinates on the Frobenious manifold in the general case of...

Topics: High Energy Physics - Theory, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1406.6661

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0.0

Jun 29, 2018
06/18

by
A. A. Bytsenko; M. Chaichian

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In this paper we analyze the quantum homological invariants (the Poincar\'e polynomials of the $\mathfrak{sl}_N$ link homology). In the case when the dimensions of homologies of appropriate topological spaces are precisely known, the procedure of the calculation of the Kovanov-Rozansky type homology, based on the Euler-Poincar\'e formula can be appreciably simplified. We express the formal character of the irreducible tensor representation of the classical groups in terms of the symmetric and...

Topics: High Energy Physics - Theory, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1602.06704

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0.0

Jun 30, 2018
06/18

by
A. A. Bytsenko; M. Chaichian

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We show that multipartite generation functions can be written in terms of the Bell polynomials (known as Fa\`a di Bruno's formula) and the Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of the hyperbolic three-geometry. We derive an infinite-product formula for the Chern-Simons partition functions and analyze appropriate q-series which leads to the construction of knot invariants. With the help of the Ruelle spectral functions symmetric and modular...

Topics: High Energy Physics - Theory, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1702.02208

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Jun 30, 2018
06/18

by
A. A. Bytsenko; M. Chaichian; M. E. X. Guimarães

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We apply the methods of homology and K-theory for branes wrapping spaces stratified fibered over hyperbolic orbifolds. In addition, we discuss the algebraic K-theory of any discrete co-compact Lie group in terms of appropriate homology and Atiyah-Hirzebruch type spectral sequence with its non-trivial lift to K-homology. We emphasize the fact that the physical D-branes properties are completely transparent within the mathematical framework of K-theory. We derive criteria for D-brane stability in...

Topics: High Energy Physics - Theory, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1408.1071

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Jun 30, 2018
06/18

by
A. A. Coley; A. MacDougall; D. D. McNutt

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$\mathcal{I}$-non-degenerate spaces are spacetimes that can be characterized uniquely by their scalar curvature invariants. The ultimate goal of the current work is to construct a basis for the scalar polynomial curvature invariants in three dimensional Lorentzian spacetimes. In particular, we seek a minimal set of algebraically independent scalar curvature invariants formed by the contraction of the Riemann tensor and its covariant derivatives up to fifth order of differentiation. We use the...

Topics: Mathematics, Differential Geometry

Source: http://arxiv.org/abs/1409.1185

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Jun 29, 2018
06/18

by
A. A. Dorogovtsev; V. V. Fomichov

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In this paper we discuss the Wasserstein distance between the n-point motions of Harris flows whose covariance functions have compact support. We prove that it can be estimated by the diameters of their support provided the latter are sufficiently small.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1606.01485